That's pretty much the flaw I read in this story. It is the assumption that a mutation only leads to a negative trait. For example, the mutation that causes sickle cell anemia also makes it where you can't get malaria so it would be a beneficial mutation in areas where malaria is prevalent. While sickle cell anemia is harmful, it isn't even as a fraction as deadly as malaria and could result in a stronger population in malaria prone areas.
The author employs multiple statistical models, all of which point to the same thing—extinction. Tell me, now that we know genes are polyconstrained, and that a beneficial mutation for one gene will be harmful to many others, how is natural selection supposed to select for the beneficial mutation without fixing the harmful mutations as well?